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Keywords:
cyclic semigroup; ordered semigroup; lattice order; idempotent element; subidempotent; superidempotent elements
cyclic semigroup; ordered semigroup; lattice order; idempotent element; subidempotent; superidempotent elements
Summary:
This paper recalls some properties of a cyclic semigroup and examines cyclic subsemigroups in a finite ordered semigroup. We prove that a partially ordered cyclic semigroup has a spiral structure which leads to a separation of three classes of such semigroups. The cardinality of the order relation is also estimated. Some results concern semigroups with a lattice order.
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